Utilizing shared frailty with the Cox proportional hazards regression: Post discharge survival analysis of CHF patients

J Biomed Inform. 2023 Apr:140:104340. doi: 10.1016/j.jbi.2023.104340. Epub 2023 Mar 17.


Understanding patients' survival probability as well as the factors affecting it constitute a significant concern for researchers and practitioners, in particular for patients with severe chronic illnesses such as congestive heart failure (CHF). CHF is a clinical syndrome characterized by comorbidities and adverse medical events. Risk stratification to identify patients most likely to die shortly after hospital discharge can improve the quality of care by better allocating organizational resources and personalized interventions. Probability assessment improves clinical decision-making, contributes to personalized care, and saves costs. Although one of the most informative indices is the time to an adverse event for each patient, commonly analyzed using survival analysis methods, these are often challenging to implement due to the complexity of the medical data. Numerous studies have used the Cox proportional hazards (PH) regression method to generate the survival distribution pattern and factors affecting survival. This model, although advantageous for survival analysis, assumes the homogeneity of the hazard ratio across patients and independence of the observations in terms of survival time. These assumptions are often violated in real-world data, especially when the dataset is composed of readmission data for chronically ill patients, since these recurring observations are inherently dependent. This study ran the Cox PH regression on a feature set selected by machine learning algorithms from a rich hospital dataset. The event modeled here was patient mortality within 90 days post-hospital discharge. The sample was composed of medical records of patients hospitalized in the Israeli Sheba Medical Center more than once, with CHF as the primary diagnosis. We modeled the survival of CHF patients using the Cox PH regression with and without the shared frailty correction that addresses the shortcomings of the Cox Model. The results of the two models of the Cox PH regression - with and without the shared frailty correction were compared. The results demonstrate that the shared frailty correction, which was statistically significant in our analysis, improved the performance of the basic Cox PH model. While this is the main contribution, we also show that this model outperforms two commonly used measures (ADHERE and EFFECT) for predicting early mortality of CHF patients. Thus, the results illustrate how applying advanced analytics can outperform traditional methods. An additional contribution is the feature set selected using machine-learning methods that is different from those used in the extant literature.

Keywords: Congestive heart failure; Cox proportional hazards regression; Shared frailty; Statistical methods; Survival analysis.

MeSH terms

  • Aftercare
  • Frailty* / diagnosis
  • Heart Failure* / diagnosis
  • Heart Failure* / therapy
  • Humans
  • Patient Discharge
  • Proportional Hazards Models
  • Survival Analysis